Imaging Throughout History
Daguerreotype (1839)
http://inventors.about.com/library/inventors/bldaguerreotype.htm
X-rays (1895)
http://inventors.about.com/library/inventors/blxray.htm
T-rays (1995)
B. B. Hu and M. C. Nuss, Opt. Lett., 20, 1716, 1995
Objectives
•Is easy to align and use
•Requires few measurements
•Generates “high” resolution pictures
Develop a T-ray imaging system that…
Outline
• T-Rays
• Principles of Tomography
• T-Ray Reflection Computed Tomography
• Discussion and Future Work
What Are T-Rays?
100 103 106 109 101
2
101
5
101
8
102
1
T-Rays
Radio Waves
Microwaves
X-Rays
Gamma Rays
Electronics Photonics
Visible Light
Hz
Why Can T-Rays Help?
0 20 40 60 80 100
Time (ps)
0.2 0.4 0.6 0.8 1.0
Frequency (THz)
0.2 0.4 0.6 0.8 1.0
Frequency (THz)
E(t) E(f) |E(f)|
•Measurement of E(t)
•Subpicosecond pulses
•Submillimeter Wavelengths
T-Rays Provide
•Depth Information
•High depth resolution
•High spatial resolution
Benefits to Imaging
Subpicosecond pulses Linear Phase Over 1 THz in Bandwidth
+ -
T-Ray System
THz Transmitter
Substrate LensFemtosecond Pulse
GaAs Substrate
DC Bias
Picometrix T-Ray Instrumentation System
Picometrix T-Ray Transmitter Module
Femtosecond Pulse
T-Ray System
T-Ray Control Box with Scanning Delay Line
Fiber Coupled Femtosecond Laser System
Sample
THz Transmitter THz Receiver
Optical Fiber
Summary of T-Rays
• Broad fractional bandwidth
• Direct measurement of E(t)
• Short wavelengths
• Unique material responses
Outline
• T-Rays
• Principles of Tomography
• T-Ray Reflection Computed Tomography
• Discussion and Future Work
Tomography
v
x
y
2D Object Slice f(x,y)
u
1D Projection p(u)
Goal of Tomography: Reconstruct a 2D or 3D image from a set of 1D measurements at multiple viewing angles
f(x,y) can be an object’s absorption, velocity, reflectivity, etc.
p(u) can be fan beam or parallel beam, transmission or reflection measurements
Examples of Tomography in Medical Imaging
http://www.radiologyinfo.org (2004)
My brain (2003)
http://pregnancy.about.com (2004)
Magnetic Resonance Imaging
X-ray Computed Tomgraphy Scan
Ultrasound
Fourier Slice Theorem
v
x
y
Object
u
Projection
kx
ky
Fourier Transform
Space Domain
Fourier Domain
The Fourier Transform of a projection is a slice in the Fourier spatial domain
Filtered Backprojection Algorithm
Each slice shares some dependency with other slices at lower frequencies
kx
ky
Ramp Filter
FBP weights every slice to reduce the dependency at lower frequencies
x
y
Filtered Projection
The filtered projection is then backprojected over the image plane
Outline
• T-Rays
• Principles of Tomography
• T-Ray Reflection Computed Tomography
• Discussion and Future Work
T-Ray Reflection Computed Tomography (TRCT)
Reflected Waves
Object Slice
Top View
Side View• Reconstruct reflectivity edge map of object’s thin tomographic slice
• Illuminate slice at multiple viewing angles and measure back reflected waveforms
• Apply filtered backprojection algorithm to retrieve image of object’s edge map
• Analagous to ultrasonic reflection computed tomography
Reflected waveforms are the convolution of the incident pulse with the projections of the object’s edge map
TRCT Imaging Setup
The object is rotated 360° in 1° increments. A measurement is made of the reflected wave at each angle.
f = 12 cm
THz Transceiver
ObjectCylindrical Lens
Tomographic Slice
Rotation Stage
Cross-Section of Test Object
Test Object: Metal Square Post
Dimensions: 1 in. x 1 in.
Material: Aluminum
Measured Waveforms
0 100 200-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
Ele
ctric
Fie
ld (
Arb
. Uni
ts)
Delay (ps)
Measured Waveforms s(,t)Reference Pulse r(t)
duupcutrts )()/2(),(
Measured waveform is the convolution of the reference pulse with the projection
Measured Waveform
Reference Pulse
Projection
Round Trip Travel Time
Image Retrieval Procedure
Step 1: Deconvolve projections p(u) from measurements s(,t)
Step 2: Retrieve reflectivity map f(x,y) from p(u)
Fourier-Wavelet Regularized Deconvolution (ForWaRD)
1. Estimate p(u) through direct Fourier inversion
2. Apply some Fourier shrinkage to reduce the amplified noise from the inversion
3. Shrink the wavelet coefficients to retrieve final estimate of p(u)
Filtered Backprojection Algorithm (FBP)
1. Filter p(u) with ramp filter
2. Backproject filtered projections across image plane
Step 2: Reconstruct Image
T-ray Image of Test Object
Photograph of Test Object
Successful recovery of object’s edges!
Dependence on Number of Viewing Angles
“Ideal” Image
0 50 100 150 200 250 300 3500.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
% C
orre
latio
n
Number of Angles
Correlation of “Ideal” Image with Reconstructed Estimate
kj kj
kjkjperfect
kj
kjkjperfect
II
II
, ,
2,2,
,
,,
%
Outline
• T-Rays
• Principles of Tomography
• T-Ray Reflection Computed Tomography
• Discussion and Future Work
Does TRCT Meet Objectives
•Is easy to align and useUses single transceiver
•Requires few measurements
360 waveforms or less
•Generates “high” resolution pictures
Resolution 100 m
Develop a T-ray imaging system that…
Possible Applications
Zandonella, C. Nature 424, 721–722 (2003).
Wallace, V. P., et. al. Faraday Discuss. 126, 255 - 263 (2004).
Medical Imaging Security
Safety
Zandonella, C. Nature 424, 721–722 (2003).
Space Shuttle Foam
Diseased Tissue
Concealed Weapon
Can TRCT Compete with X-rays?
TRCT X-rays
100 m spatial resolution
• Low health risk
• High contrast
• Spectroscopic information
• Potential Uses: Security, quality control, medical imaging
• < 10 m spatial resolution
• Potential health risks
• Lower contrast
• Narrow bandwidth
• Current Uses: Medical imaging, security
Answer: Application dependent
Future System Improvements
• Actual Transceiver Module
• Increase Signal to Noise Ratio
• Acquisition Speed: – 5-6 sec./meas. 100 msec./meas.
• 3-D Imaging
• Automated Software
Future Algorithm Improvements
Inhomogeneous Velocity Incomplete Angle Data
Distortion of aluminum rods from incorrect velocity model
Reconstruction artifacts from incomplete data
Other Improvements
• Computational time
• Deconvolution method
• Velocity estimation
Summary
• Developed a new reflection mode T-ray imaging system
• Tested system’s capabilities on a diverse set of objects
• Compared TRCT to other commercially available imaging systems
• Suggested improvements for imaging system and reconstruction algorithm
Other Work
THz detector
THz transmitter
Sample cell
-8 -6 -4 -2 0 2 4 6 81E-6
1E-5
1E-4
1E-3
0.01
0.1
P(E
r/),
P(E
i/)
E/
NO free parameters!
The Multiple Scattering of Broadband Terahertz Pulses
THz Circular Synthetic Aperture Radar
Publications
1. J. Pearce, Z. Jian and D. M. Mittleman, “Spectral shifts as a signature of
the onset of diffusion of broadband terahertz pulses,” Optics Letters,
accepted (2004).
2. J. Pearce, Z. Jian, and D. Mittleman, “Propagation of terahertz pulses in
random media,” Philosophical Transactions A, 362, 301 (2004).
3. J. Pearce, Z. Jian, and D. Mittleman, “Statistics of multiply scattered
broadband terahertz pulses,” Physical Review Letters, 91, 043903 (2003).
4. J. Pearce and D. Mittleman, “Scale model experimentation: Using
terahertz pulses to study light scattering,” Physics in Medicine and
Biology, 47, 3823 (2002).
5. J. Pearce and D. Mittleman, “Definition of the Fresnel zone for broadband
radiation,” Physical Review E, 66, 056602 (2002).
6. J. Pearce and D. Mittleman, “The propagation of single-cycle THz pulses
in random media,” Optics Letters, 26, 2002 (2001).